Helium cooling of Silicon Pixel Detector for Mu3e Experiment
Master Thesis
University of Applied Sciences and Arts Northwestern Switzerland Institute of Thermal and Fluid Engineering, ITFE
Master of Science FHNW in Engineering Specialisation in Energy and Environment 4th March, 2019
Student Project supervision Project partner Marin Deflorin Prof. Dr. Beat Ribi Mu3e
marin.deflorin@students.fhnw.ch Prof. Dr. Peter Stuber Dr. Frank Meier Aeschbacher
marin.deflorin@gmail.com Prof. Dr. Daniel Weiss
Acknowledgements
This master thesis was written during my studies for the Master of Science in Engineering at the University of Applied Sciences and Arts Northwestern Switzerland. From September 2018 to February 2019 I worked on the helium cooling system of the Mu3e experiment. At this point I would like to thank all involved people and friends for their support. This work would not be feasible to such an extent without the countless aids. Special thanks goes to:
• Frank Meier Aeschbacher and Mu3e collaboration
• Beat Ribi, Peter Stuber and Daniel Weiss
• Patrick Lüscher
• Edgar Brodmann
• Raphael Brunner
• Nino Degiampietro, Katharina Domnanich, Elias Mai, Sebastian Schmid, Elias Waldvogel
• Soraya Bonvin
March 2019, Marin Deflorin
Abstract
The Mu3e experiment is searching for the rare decay of a muon into two positrons and an electron. This would provide evidence of a new physics beyond the standard model of particle physics. The Mu3e experiment consists of three different detectors. A tracker made of thin silicon chips is used for vertex and momentum measurements and combined with two separate timing detectors. The thin silicon chips have an expected heat dissipation of 250−400mW/cm2
and their temperature should not exceed 70◦C. Several cooling flows with an inlet temperature of 4◦C are planned to stay in within this temperature limit. The optimal fluid for the experiment is helium, as it minimises the scattering of charged particles and is an excellent coolant.
In this thesis, the cooling of the silicon chips (MuPix) with helium was investigated in detail.
At first, estimations were performed to determine an appropriate modelling approach for the simulation, and also to a first results of the occurring temperature.
A thermo-mechanical mockup of the Mu3e detector was experimentally investigated. The mockup was instrumented to measure the mass flows, temperatures, pressure drops, displace- ment of the detector as well as some other quantities. For the first measurements air was used as a coolant at a similar Reynolds number and temperature increase. Later the tests were repeated with helium to get the desired results.
CFD simulations were used to investigate the flow fields and determine the potential for im- provement of the cooling system. Several iterations with optimised flow geometries were carried out until a geometry was found which ensures a more uniform cooling.
The comparison between the experimental results and the simulation proves that the cooling of the silicon chips can be performed in the specified range. Additionally, a simulation of the system was performed to investigate the placement of the control valves. The results were summarised at the end of the report including suggestions for improvements and possible further steps are described.
Nomenclature vi
Acronyms ix
1 Introduction 1
1.1 Mu3e Experiment . . . 2
1.2 Progression of cooling system . . . 2
1.3 Goal . . . 3
1.4 Approach . . . 4
2 Cooling system 7 2.1 Experiment components . . . 7
2.2 Coolant . . . 9
2.3 Helium cooling . . . 9
2.4 Material properties . . . 14
3 Theoretical fundamentals and analytical study 17 3.1 Joule-Thomson Effect . . . 17
3.2 Passage of charged particles through matter . . . 18
3.3 Cooling . . . 19
3.4 Dimension analysis . . . 21
3.5 Estimation of physical parameters . . . 22
3.6 Cooling analysis . . . 25
3.7 Conclusions of analytical study . . . 31
4 CFD Simulation 33 4.1 Overview . . . 33
4.2 Layers 1 & 2 . . . 43
4.3 Layers 3 & 4 . . . 58
4.4 V-folds layer 3 & 4 . . . 61
4.5 Gap layer 3 & 4 . . . 65
4.6 Gap layer 3 & SciFi . . . 69
4.7 Layers 3 & 4 coupled . . . 72
5 Measurements 83
5.1 Measurement model . . . 83
5.2 Mockup of layers 1 & 2 . . . 86
5.3 Equipment and setup . . . 93
5.4 Data evaluation . . . 112
5.5 Diverse observations . . . 113
5.6 Results . . . 124
6 System simulation 133 6.1 Approach . . . 133
6.2 Layer 1 & 2 . . . 134
6.3 Cooling plant concept . . . 139
7 Comparison of results 141 7.1 Simplifications . . . 141
7.2 Wall heat transfer coefficient . . . 141
7.3 Temperature distribution . . . 142
7.4 Dimensionless temperature . . . 144
7.5 Discussion . . . 145
8 Summary and Outlook 147 8.1 Outlook . . . 149
8.2 Goal . . . 152
8.3 Review . . . 153
List of Figures 157
List of Tables 160
A Project management 162
B Simulation 189
C Measurements 192
D Digital appendix 198
Symbols
A Area m2
cp Specific heat capacity at constant pressure J/kg·K
D Diameter m
g Gravitational acceleration of Earth m/s2
k Extended uncertainty factor −
l Length m
˙
m Mass flow g/s
Q˙ Total heat load W
˙
q Heat load per surface mW/cm2
˙
q Heat load per volume W/m3
R Resistance Ω
T Temperature ◦C or K
U Perimeter mm
w Velocity m/s
x Position along layer mm
z Distance from midplane mm
Greek symbols
α Temperature coefficient of resistance 1/K
α Wall heat transfer coefficient W/m2·K
∆ Difference −
Emissivity coefficient −
γ Coefficient of thermal expansion 1/K
λ Thermal conductivity W/m·K
µ Dynamic viscosity kg/m·s
µJT Joule-Thompson coefficient K/bar
ν Kinematic viscosity m2/s
ρ Density kg/m3
ρ Specific resistance Ωmm2/m
σ Stefan-Boltzmann-constant W/m2·T4
Dimensionless numbers
Bi Biot number −
Ma Mach number −
Nu Nusselt number −
Π Dimensionless number −
Pr Prandtl number −
Re Reynolds number −
Ri Richardson number −
y+ Dimensionless wall distance −
Indices
0 Inlet
∞ Temperature far away from wall
a Araldite
cor Corrected
d Divider
f Fluid
g Annular gap
h Hydraulic
I Current
i Inlet
Mesh Mesh
MuPix Mupix
ov Overlap
o Outlet
p Polymide
q Constant heat flux on wall
R Resistance
TC Thermocouple
Th Thermal
U Voltage
w Wall
x Local
Particle Physics
βc Velocity of incident particle m/s
e+ Positron
e− Electron
µ+ Muon
p Momentum of incident particle kg·m/s
x Mass per unit area g/cm2
X0 Radiation length g/cm2
z Charge number of incident particle −
Acronyms
CAD Computer-aided design
CFD Computational Fluid Dynamics
CLFV charged lepton flavor violating
DAQ Data acquisition
E+H Endress + Hauser
EA Elektro-Automatik
FHNW University of Applied Sciences and Arts Northwestern Switzerland
GUM Guide to the Uncertainty in Measurement
ITFE Institute of Thermal and Fluid Engineering
G12 gap flow between layers 1 & 2
G34 gap flow between layers 3 & 4
G3S gap flow between layer 3 & SciFi G3T gap flow between layer 3 & tile detector
NI National Instruments
POM Polyoxymethylen
PSI Paul Scherrer Institute
SciFi Scintillating Fibre
SM Standard Model
V3 V-fold of layer 3
V34 V-fold of layers 3 & 4
V4 V-fold of layer 4
1 Introduction
The Mu3e experiment goal is to search for the decay of a muon into two positrons and one electron, which would give evidence of new physics beyond the Standard Model (SM) of particle physics. This fundamental physics experiment is a big challenge as most of the parts are new developments. Such a complex experiment is not only connected with scientific challenges in the field of physics, moreover the construction and assembly of components as well as the setup of the cooling system require tremendous engineering skills. The Mu3e experiment requires minimal material use, as otherwise the particles are deflected and therefore the required precision could not be achieved. One of the most crucial questions is the establishment of a gaseous helium cooling for ultra thin silicon detectors, encompassing a total surface of about 1 m2.
Mu3e is a collaboration which started in 2012 and currently consists of several European in- stitutes which are based in Bristol, Genève, Heidelberg, Karlsruhe, Liverpool, London, Main, Oxford, Villigen and Zürich. The experimental setup will be commissioned at the premises of Paul Scherrer Institute (PSI) and currently entered phase I of the building stage. To realise further development and a functional evaluation of the cooling system, the Mu3e collabora- tion and especially Frank Meier Aeschbacher approached the University of Applied Sciences and Arts Northwestern Switzerland (FHNW) and the Institute of Thermal and Fluid Engineer- ing (ITFE) for a cooperation. The first results of this mutual effort are summarised in this thesis, whereby the main focus was laid on the technical realisability of the helium cooling. For people interested into the muon decay and the experiment, detailed information can be found on www.psi.ch/mu3e/.
The focus of this thesis is the development of a cooling system for the MuPix chips of the Mu3e experiment, which are basically silicon chips with a thickness of 50µm on a polymide layer.
These chips have a heat dissipation of up to 400 W/m2 and must be cooled below 70◦C with a medium fulfilling the following requirements, low atomic number, good cooling properties and be inert. Helium was chosen because it best meets all the prerequisites.
In the next sections, the basic concept of the Mu3e experiment will be briefly explained, followed by a summary of previous projects on the helium cooling system. Then the goals as well as the approach will be discussed and finally an outlook over the whole thesis will be given.
1.1 Mu3e Experiment
The Mu3e experiment intents to search for the charged lepton flavor violating (CLFV) decay µ+→e+e−e+. The goal is to either detect the decay or set a new branching ratio limit of 10−16 at a confidence level of 90 %. This would be four orders of magnitude lower than the previously performed search by the SINDRUM experiment [1]. In the Standard Model of particle physics the decay is suppressed with branching ratio under 10−54, so any observation of the decay would be a sign for New Physics beyond the Standard Model. Different new physics models postulate the CLFV within the achievable limits of the Mu3e Experiment. The currently most intense source of low-energy muons is situated at PSI with a maximum muon rate of 1·108Hz envisaged to be used during phase I of the project. A beam with higher intensity is currently under development and will probably be only available after 2025 for phase II experiments. In order to reach the aimed branching ratio, one year of data collection with a muon rate of 2·109Hz will be required. Besides a high intensity muon beam, other crucial parameters, such as excellent timing, vertex and momentum resolution of the electrons and positrons are mandatory. The newly developed detector technology necessitates an extensive testing and improvement of the experimental setup and facilitates the collection of data within the next two years.
There are three different detectors with different functions which are described in section 2.1.
The experimental setup is inside of a large superconducting magnet with an inner diameter of 1 m and a field intensity of 1 T which is required to keep the particle on a circular track. The detectors are positioned in a way to track as many particles as possible.
1.2 Progression of cooling system
The cooling system has already been analysed by a number of projects mainly performed at the University of Heidelberg. Most of them analysed the possibility of cooling the MuPix chips with helium with the then current version of design and specification. Their combined efforts led to the development of the current cooling concept Zimmermann [2] has first investigated the possibilities of a helium cooling for the Mu3e experiment. This included Computational Fluid Dynamics (CFD) simulation over one MuPix chip as well as measurements of a single silicon chip. Huxold [3] followed with an experimental setup with heatable mockup with accurate dimensions but only one global flow over all layers. Ng [4] has analysed and simulated both the inner and outer detector part and introduced the V-folds thereby increasing the stability of the outer layer and enabling a local cooling channel. The simulation model of Ng has been further developed by Herkert [5] and enhanced by adding a heatable model with the present geometry.
The final geometry of the detector was designed after this works and was mostly finalised at the beginning of 2018. Tormann [6] used this geometry for new CFD simulations which showed that
1.3 Goal
there are some backflow regions which are causing high temperature especially on layers 1 & 2.
Without this previous project, the helium cooling system would not be in such an advanced state.
This project is the first one where a heatable mockup with the final geometry of layers 1 & 2 is available. This mock-up has some little simplifications as there are aluminium heaters used, instead of the MuPix chips. The mock-up of layers 3 & 4 is not available until now due to production delays.
1.3 Goal
The following goals are a summary from the project clarification which can be found in ap- pendix A.2. Main goals of the project are to analyse the helium cooling of the MuPix chips, optimise parts which could affect the experiment and create a concept for the control and reg- ulation system. In the following list the sub-goals can be found:
Temperature The temperature of the MuPix chip should not exceed 70◦C with a heat dissipation of 400mW/cm2.
Verfication Verification of the cooling results of the Layer 1/2 and 3/4 ob- tained in previous works.
Instrumentation Instrumentation of the mockup for validation of the CFD and flow system-simulations.
Validation Validation of the simulation results with measurements on the mockup.
Optimisation Optimise the cooling of the Layer 1/2 and 3/4 if the temperature is too high or if other unacceptable states occur, e.g. oscillations that may trigger mechanical vibrations or stress.
Thermal deformation Thermal deformation of the flexprint has to be investigated and the influence of it onto the cooling behaviour.
Flow system Characterisation of helium flow through the whole system with the pressure drop and system behaviour.
Control concept Develop a control concept for the helium cooling circuit with focus on start-up and shut-down phases.
The project task can be found in appendix A.1.
1.4 Approach
Based on these goals, which were agreed upon at the beginning of the project, different tasks were defined and are listed in figure 1.1. There are three main work packages which are investigating the helium cooling system of the Mu3e experiment. At the beginning, CFD simulations have been planned as the geometrical data were available and could also be compared with the results of Tormann [6]. The second package includes the measurements with the instrumentation. As the mockup was still in manufacturing process this was set after the simulation. The last package is to analyse the helium cooling system behaviour which includes the regulation of the different flow and determine whether control elements must be placed inside the magnet or not.
1.4Approach
Figure 1.1: Task structure diagram.
5
In this thesis the cooling concept for the Mu3e pixel detector has been investigated using CFD simulation, measurements on a full-scale model of one part of the detector and some system analysis for the overall cooling circuit. The results of the simulations have been compared with the measurements. Chapter 2 gives an overview of the cooling system, the relevant components as well as material properties which are used in the following chapters. In chapter 3 theoretical fundamentals used for this thesis and analytical study of the cooling behaviour are explained.
Chapter 4 describes the CFD simulation and optimisation of different geometries to obtain a more regular flow and cooling. In chapter 5 the measurement setup and results are shown. The system analysis which is looking on the control concept is described in chapter 6. The results of the simulations and the experiment are then compared and discussed in chapter 7. Finally, chapter 8 is concluding this thesis with an overall summary, open tasks and thoughts for the further development of the cooling system.
2 Cooling system
In this chapter, general information about the cooling system is given to provide an overview.
Later, this knowledge will be used for the simulation, measurement and system modelling.
A short browse through this chapter is recommended as it gives information common to all subsequent chapters. Furthermore, it gives an understanding of the cooling system and the components included. The whole experiment is explained in section 1.1, which describes the goals of the Mu3e experiment.
2.1 Experiment components
The relevant components for the helium cooling are the MuPix1 chips which allow the detection of charged particles (here: electrons and positrons). The MuPix chips provide a high vertex and momentum resolution but insufficient timing resolution, which is important for distinguishing tracks from different decays occurring at almost the same time. Therefore, there are two different sensors with high time resolution but low spacial resolution. Figure 2.1a shows a sketch of all detectors as well as the target and the µbeam. One theoretical muon decay into two positrons (red) and one electron (blue) is displayed. The particles are first passing the layers 1 & 2 followed by the Scintillating Fibre (SciFi) detector, layers 3 & 4 of the central part. Due to the magnetic field, the particles are recurling and optimally passing the up- or downstream layers 3 & 4 and finally hitting into the tile detector. The MuPix layers as well as the SciFi must be made of very thin material to reduce the scattering of the charged particles2. For the tile detector there is no such requirements as it is placed at the end of the recurling particle trajectories.
For the track reconstruction data from all three detectors are combined. The reconstruction itself is using graphics processing units and only interesting events are stored for later analysis to reduce data volume.
1Silicon detector which is further described in section 2.3.2.
2(Charged particles passing through matter are deflected, which is dependent on the passed matter, see also section 3.2.)
Layer 3 & 4
Tile detector
µbeam
Layer 1 & 2 Scintillating Fibre
Target (a) Cute through all detectors and target.
(b) Cut through the target and parts of the central detector.
Figure 2.1: Detector used for the Mu3e experiment with the MuPix sensor on the layers 1-4, Scintillating Fibre and the tile detector. Additionally, a theoretical particle track of a muon decay into two positrons and one electron is shown. [7]
2.1.1 Deviation of charged particles
The electrons and positrons fly through the different detectors and should optimally collide with as few matter as possible to enable a precise tracking of the trajectories. In section 3.2 the deflection angle of a charged particle passing through matter is explained. Therefore, it is required to have small radiation length3 for all parts which are passed by the particles. The MuPix chips have a radiation length ofx/X0 ≈0.115 % and the particles fly through a maximum of six layers. The SciFi detector has a thickness of under 100µm and a radiation length of
x/X0 <0.2 % which is a little higher than the one of the MuPix layer but is less critical as only one detector is present.
3Indicator of the deflection angle of charged particles passing this matter. Further information in section 3.2.
2.2 Coolant
2.2 Coolant
The limitations restricting the detector in terms of layer thickness are also valid for the coolant.
It can mainly be influenced by the used fluid which should have a good cooling capacity, low chemical reactivity as well as a small radiation length. Assuming the flight length of one particle from target to the tile detector to 1 m and that the coolant is filling all cavities, the radiation length of coolant can be evaluated. Nitrogen has then a radiation length of x/X0 ≈ 0.3 %. A lighter element such as helium has a radiation length of 0.019 % which increases the accuracy of the experiment and is therefore preferred.
Additionally, helium is a good coolant with high heat conductivity compared to other gases and is chemically stable. There is only Hydrogen which has better cooling properties than helium.
It has a 20 % higher heat conductivity and a 2.7 times higher heat capacity. But hydrogen is explosive in combination with air which would require high safety precaution for the whole experiment. Therefore, helium is the best available coolant for the Mu3e experiment.
2.3 Helium cooling
The experiment has mainly two different cooling circuits. Parts that are passed by the electrons and positrons require a small radiation length to minimise the multiple coulomb scattering.
Therefore, these parts are cooled by gaseous helium. Other parts as the tile detector or readout parts of the SciFi can be cooled with liquid water as these parts are not passed by the tracked particles. In this thesis only the helium flows are considered which are shown in figure 2.2. The parts A & C (up- & downstream) are principally the same just mirrored on the midplane. They are consisting of two MuPix layers (3 & 4) which are cooled with three helium flows. The part B (centre) has additionally to the outer layers 3 & 4 the inner MuPix layers 1 & 2 which are cooled with one gap flow. Those layers consists of several segments which are described in the next section.
The V-folds flow is flowing inside of a polymide fold glued onto the layers 3 & 4 and provides directly a cooling flow to the chips. The gap flows is flowing in between two layers or between a layer another detector.
2Coolingsystem Part B (Centre)
Part A (Upstream) Part C (Downstream)
Global V-fold layer 4 Gap layer 3 & 4 V-fold layer 3 Gap layer 3 & SciFi
Silicon layer 4
Silicon layer 3 Silicon layer 2Silicon layer 1
Gap layer 1 & 2
Target z
Figure 2.2: Helium cooling system of the silicon chips with detail of the centre part.
10
2.3 Helium cooling 2.3.1 Layer segments
Each of the four layers consists of several segments. One segment of the mockup is shown in figure 2.3. One segment consists of multiple MuPix chips which are aligned next to each other.
The number of chips over the segment length and the number of segments per layer are shown in table 2.1. The diameter is the distance of two segments on the opposite side. For the layers 1 & 2 6 chips are aligned, while the layers 3 & 4 have a total of 17 or 18 chips in row.
Table 2.1: Dimensions of the different layers and segments.
Layer 1 2 3 4
Number of segments per layer 8 10 24 28 Number of chips per segment 6 6 17 18 Layer "diameter" [mm] 46 59 144 170
Layer length [mm] 120 120 340 360
Figure 2.3: One segment of MuPix chips of layers 1 & 2 with 6 Mupix chips.
2.3.2 MuPix Chips
The MuPix chips are the part which have to be mainly cooled with helium. These chips are detecting passing electrons and positrons and have a high vertex and momentum resolution which is needed for the trajectory reconstruction. They are still in development and therefore the final heat dissipation of the chips is not available until now. It is expected that the chips will have a heat dissipation of 250mW/cm2 but the cooling system should be designed to keep the chip temperature under 70◦C with a heat dissipation of 400mW/cm2. This is representing the worst case scenario.
The chips have a dimension of 20×23 mm2 with a sensitive area which is only 20×20 mm2. This part is called detector area. The 3×20 mm2 area consists of digital read out and power lines. This inactive part is called periphery and has a higher heat dissipation as the detector area. The share of the heat has been estimated to be equal in terms of total heat for both parts which means that the periphery has a higher heat dissipation per surface than the detector.
This is further explained in section 4.1.5.
The mockup which is used for the experiment has tape heater4, where only a constant heat load can be applied. As the simulation will be compared with the experimental results, the simulation will be performed with and without the high heat dissipation of the periphery.
In previous works both heat dissipations (250&400mW/cm2) have been simulated and then com- pared. As the temperature increase is mainly dependent on the heat dissipation, only the worst case with 400mW/cm2 will be simulated. To evaluate the temperature with another heat dissi- pation it can be linearly scaled, as long as the heat dissipation is smaller or in the same range as the worst case. Figure 2.4 shows the maximal and average temperature of the MuPix chips from a simulation which is in good agreement with a linear approximation.
0 50 100 150 200 250 300 350 400 450 500 550
0 20 40 60 80
Heat load [mW/cm2] Temperature[◦ C]
Maximum temperature Average temperature
Figure 2.4: Temperature of MuPix chips depending on different heat dissipations.
The layers 1 to 4 showed in figure 2.2 have all different number of MuPix chips on them.
Table 2.2 shows the number of chips per layer as well as the heat dissipation of each layer with the two different heat loads. The total heat dissipation with 400mW/cm2 of all MuPix chips is approximately 5.5 kW.
Table 2.2: Absolute heat load per layer.
Layer Total heat load [W] (250/400)
1 (48) 54.9 87.9
2 (60) 68.7 109.9
3 (408) 466.9 747.0
4 (504) 576.7 922.7
Total Centre (B) 1162.8 1866.6
Total (ABC) 3416.6 5484.5
4Segments with inactive steel plates and aluminium resistance to emulate the heat dissipation of MuPix chips.
2.3 Helium cooling 2.3.3 Flows
For all the flows short names have been used, especially in the CFD simulation chapter. The gap flow as code G with the included layers, so the G12 is the gap flow between layers 1 & 2, G3S between layer 3 and SciFi etcetera. The following list shows the most used acronyms for the flows and parts:
V3 V-fold of layer 3 V4 V-fold of layer 3
G34 gap flow between layers 3 & 4 G3S gap flow between layer 3 & SciFi G3T gap flow between layer 3 & tile detector Part A Upstream layers 3 & 4
Part B Center layers 3 & 4 Part C Downstream layers 3 & 4
The flows which have been shown in figure 2.2 have different mass flows through their volume.
For most flows the average velocity has been set to 10m/swhich has been taken from the previous project. The V-fold of layers 3 & 4 (V34) flow velocity has been set to 20m/sas the area is quite small. The global flow has only a velocity of 0.5m/sbut increases over the length of the detector as all gap flows of the outer layers are merged into the global flow. The inner diameter of the magnet is around 1 m which would result in a high mass flow with the specified velocity without essentially increasing the cooling capacity. Therefore, a mylar tube with a diameter of 0.3 m is proposed for the global flow to obtain a smaller area with helium flow.
Table 2.3 shows the different flows with the mass flows and also the required pressure at the in- & outlet. The striked global flow shows the required mass flow without a mylar tube which would double the total required mass flow. The indicated pressure drops have been taken from simulation, which were only performed until the end of the straight 3D printed in- & outlet geometries. The pressure drop of the tubing which lead out of the magnet as well as the change in diameter and bending in the tube is not considered in the pressure drop. Therefore, the required pressure drop will be higher.
Table 2.3: Helium mass flow through different cooling sections. Pressure levels are taken CFD simulation with the optimised parts which have higher drops than the original ones.
Flow # Inlet mass flow Inlet pressure Outlet pressure Velocity
[g/s] [mbar] [mbar] [m/s]
G12 1 2.0 40 −40 10
G3S 1 6.9 25 0 10
G3T 2 5.7 28 0 10
G34 3 7.6 25 0 10
V3 3 1.3 90 −90 20
V4 3 1.5 80 −80 20
Global (D= 0.3 m) 1 4.0 0.3 0 0.5
Global (D= 1 m) 0 62.4 0.5
Total 55.5
2.4 Material properties
The material properties shown here are used for all following chapter.
2.4.1 Gas
Properties of helium are relatively constant with differing pressure in the used range but show some dependency on the temperature. The pressure is around atmospheric pressure for all parts of the cooling system which were analysed. In the range of 0−100◦C the viscosity and thermal conductivity of helium are changing up to 35 %. The viscosity and thermal conductivity have therefore been approximated with a linear function in this region. The largest deviation from the linearisation is 0.25 %. Same has also been applied for air which has a similar deviation due to the linearisation. The used standard conditions are 20◦C and 1 bar. This linear approximations were used for the CFD simulations.
2.4 Material properties
Table 2.4: Properties of helium and dry air used for simulations and estimations [8].
Property Helium Air Unit
Molar mass 4.0 28.96 [g/mol]
Thermal conductivity 0.154 0.026 [W/m·K]
Dynamic viscosity 19.6·10−6 18.2·10−6 [kg/m·s]
Specific heat capacity 5193.2 1006.1 [J/kg·K]
Density 0.164 1.19 kg/m3
Velocity of sound 1016 346 [m/s]
Temperature and pressure dependency
Thermal Conductivity 0.14 + 3.5·10−4·T 0.024 + 7.3·10−5·T [W/m·K]
Dynamic viscosity 18.7·10−6+ 4.5·10−8·T 17.2·10−6+ 4.7·10−8·T [kg/m·s]
Density Ideal gas Ideal gas kg/m3
2.4.2 Air humidity
The air properties from table 2.4 are for dry air but in the experiment the laboratory air has a relative humidity between 35 and 60 % RH which gives a mass fraction of around 0.4−0.9 %.
This increases the specific heat capacity by less than 1 % as well as the other quantities and is therefore neglected in this thesis.
2.4.3 Solid
The solid properties are less temperature dependent than the one of the gases. For the range used in this thesis the properties have been set to a constant value.
Table 2.5: Properties of silicon [9], polymide [10], steel (1.4310) [11] and araldite [12] used for simulations and estimations.
Property Silicon Polymide Steel Araldite Unit
Molar mass 28.086 [g/mol]
Thermal Conductivity 149 0.12 15 0.22 [W/m·K]
Specific Heat Capacity 783.3 1090 500 [J/kg·K]
Density 2.33 1.42 7.9 kg/m3
Thermal expansion 2.56 30-60 16 10−6K
3 Theoretical fundamentals and analytical study
This chapter is describing most used theoretical fundamentals together with analytical study of the cooling system. This is not including the fundamentals of the Mu3e experiment which would go far over the knowledge of a mechanical engineer and is not necessary for the understanding of the cooling system which is analysed here.
3.1 Joule-Thomson Effect
The Joule-Thomson effect is a real gas behaviour of adiabatically expanding gases. The molecules of the gas at low temperatures are attracted by each other and while expanding they move away from each other. This requires energy, which is taken from the kinetic energy of the molecules, which become cooler as a result. On the other hand, at high temperatures the molecule try to repulse from each other. The separation releases energy, which is converted into kinetic energy of the molecules. Therefore, the behaviour during an expansion is a function of the current temperature but also of the current pressure as this defines the distance between the molecules.
This behaviour is called the Joule-Thomson effect which is described with the Joule-Thomson coefficientµJTwith the unit K/bar. At room-temperature and 1 bar only 3 gases have a repulsion of the molecules which gives them a negative Joule-Thomson coefficient, namely hydrogen, helium and neon. Figure 3.1 shows the µJT depending on the temperature for different gases.
Helium has the lowest inversion temperature at 34 K, where the attraction forces is equal to repulsion. For ideal gases the Joule-Thomson coefficient is zero.
0 100 200 300 400 500 600 700 800 0
0.2 0.4 0.6
Temperature [K]
Joule-ThomsoncoefficientµJT[K/bar]
Helium Hydrogen NeonAir Nitrogen Oxygen
Figure 3.1: Joule-Thomson coefficient of different gases at 1 bar depending on the tempera- ture. [8]
3.2 Passage of charged particles through matter
Charged particles like electrons or positrons passing through matter are deflected by many small-angle scatters, the nuclei and the electrons of atoms. The net scattering resulting of this multiple small-scatter follows a distribution that can be approximated by a Gaussian curve.
This distribution is disturbed by "hard" scatters which produces a deviation at the far end of the curve. Figure 3.2 shows a charged particle passing through matter and the quantities used to describe the deviation. For a thin detector as used in the Mu3e experiment the y and z displacement can be neglected and only the angle deviation θ must be considered.
x
x/2
splane
θplane yplane
Ψplane
Figure 3.2: Used quantities used for multiple Coulomb scattering modified from [13].
3.3 Cooling
The width of the Gaussian distribution of the deviation angle can be estimated as
θ0 = 13.6 MeV βc·p z
r x X0
"
1 + 0.038·ln( x·z2 X0·β2)
#
(3.1) wherep,βcand zare the momentum, velocity and charge number of the incident particle. The radiation length X0 describes the mean distance over which a high energy electron loses all but 1/e of its energy by bremsstrahlung. The radiation length is dependent on the atomic number.
Light materials have a higher radiation length which leads to less scatters and lower deviation angle. For experiments observing the trajectories of charged particle a high radiation length is crucial to increase the precision.
This section has been summarised out of “Review of Particle Physics” [13].
3.3 Cooling
The analytical study of the cooling system is only performed for the gap flow between layers 1 & 2 as it only contains one cooling flow. Layers 3 & 4 have several cooling flows which make an analytical study more complex and less accurate.
3.3.1 Illustration of the system
The cooling system of the MuPix chips is simplified here for the analytical study. Figure 3.3 shows the inflow geometry in red as well as the gap flow between layers 1 & 2 (G12) in transparent grey. After the gap flow the outflow geometry follows which is not displayed here. The in- and outflow are neglected in this chapter as it causes some irregular flow which can hardly be considered.
Figure 3.3: Inflow geometry and gap flow between layers 1 & 2.
The octagons and decagons of layers 1 and 2 are simplified by a tube with diameters correspond- ing to the edge distances illustrated in figure 3.4. For a tube there are analytical approximations which can be used for a first estimation as well as a reference for the simulations. Two MuPix chips are also shown, which are overlapping the outer decagon and the inner octagon.
Original cross sectionSimplified cross section Overlap of MuPix
Figure 3.4: Simplified cross section of gap flow between layers 1 & 2 for analytical study.
The simplified geometry is a tube with a length of 120 mm, inner diameter ofDi = 46 mm and outer diameter of Do = 59 mm. The heat dissipation of the chip is applied onto the whole wall but corrected to obtain the total heat which is emitted by the MuPix chips.
3.4 Dimension analysis
3.4 Dimension analysis
With a dimensional analysis of the simplified case the relevant non-dimensional number can be identified. Figure 3.5 shows the dimensions that have been evaluated to be relevant for the cooling process. There are in total 13 dimensions and 4 physical units ( [K,kg,s,m]). As the specific heat capacity is only used together with the density this two are combined. The heat dissipation ˙q is not considered for the non-dimensional analysis. This gives a total of six non-dimensional numbers which can be found with Buckingham-Π theorem.
Ts,cps,ρs,λs,α Tf,cpf,ρf,λf,νf w
lf
ls
˙ q
Figure 3.5: Annular flow considered for the analytical study of the gap flow between layers 1 & 2.
The six non-dimensional numbers are shown below. Not all these numbers have been used in this thesis. Π3−6 have been used for the estimation followed in the next sections.
Π1= Tf
Ts (3.2)
Π2= cpf·ρf
cps·ρs (3.3)
Π3 = Nu = α·lf
λf (3.4)
Π4= Pr = ν·ρf·cpf
λf (3.5)
Π5= Re = lf ·w
ν (3.6)
Π6 = Bi = α·ls
λs (3.7)
3.5 Estimation of physical parameters
For the cooling analysis, CFD simulations and measurements it is important to know the present physical conditions. This includes mainly flow conditions and thermal properties.
Table 3.1: Data used for the estimation of non-dimensional number.
Property Value Unit Source
Length scale l 13 [mm] Do−Di
Velocityw 10 [m/s]
Wall temperature Tw 70 [◦C]
Fluid temperature T0 0 [◦C]
Coefficient of thermal expansion Helium γ 3.41·10−3 [1/K] [8]
Mach number 0.06−0.15 [−]
Reynolds number 1090−2350 [−]
Richardson number 3.04·10−4 [−]
3.5.1 Mach number
The Mach number is used to estimate if compressible effects can be expected. The Mach number for the high velocity (60m/s) in the inflow tubes of G12 is Ma = 0.06. The inflow slots, where the fluid is directed into the gap has the highest velocity which goes up to 150m/swhich is still far away from Ma = 0.3. For layers 3 & 4 the velocities are quite similar. Therefore, compressible effects of the fluid is not expected and will be neglected in this thesis.
Ma = w
c (3.8)
3.5.2 Reynolds number
The Reynolds number is computed to give an idea if the flow is rather laminar, turbulent or in a transitional region. The critical Reynolds number for circular tubes and similar forms is Recrit ≈ 2300. Under Recrit the flow stays always laminar. The transition region is between 2300<Re<104 where the flow is influenced by the inflow conditions. A flow with a Reynolds number over 104 is certainly turbulent. For an annular gap flow the critical Reynolds number is the same when using as characteristic length the difference of the diameters. [14]
Re = Dh·ρ·w
µ (3.9)
Here only the Reynolds number of G12 are estimated but are characteristic for all flows, which are in a similar range. In chapter 4 the Reynolds number of every flow is evaluated. There are
3.5 Estimation of physical parameters
two main regions which have different Reynolds number which are shown in figure 3.3. The red inflow region has a smaller area and has therefore higher velocity, whereas the grey transparent gap flow has lower velocities.
Inflow tubes
For the inflow tubes the hydraulic diameter (see equation (3.10)) is used for the characteristic diameter which is 4.7 mm. The average flow velocity is 60.4 m/s which results in a Re = 2350.
This is just above Recrit and therefore in the transition region. The flow will probably stay laminar in the inflow tubes.
Dh = 4·A
U (3.10)
Annular gap flow
The length scale in the gap is defined following VDI-Wärmeatlas [14] which is the difference of the diameters (see equation (3.13)). The hydraulic diameter of the annular gap flow is therefore 13 mm and has an average flow velocity of 10 m/s. This results in a Reynolds number of 1090 which is clearly under the critical Reynolds number. The annular gap flow will stay laminar.
3.5.3 Richardson number
Another relevant number is the Richardson number (see equation (3.11)) which is basically comparing the natural convection to the forced convection. With small Richardson numbers the natural convection can be neglected and with high numbers the forced convection.
For gap flow between layers 1 & 2 the Richardson number is small and is therefore indicating that the natural convection can be neglected and therefore also the gravitation and thermal expansion of the gas. For the other flows and air as fluid the Richardson number is in a similar range.
Ri = g·γ·(Tw−T0)·l
w2 (3.11)
3.5.4 Heat radiation
All bodies with a temperature higher than the absolute zero is emitting thermal radiation. This radiation has mostly wavelength in the infrared region. When a body is in thermal equilibrium with its surroundings, the thermal radiation emitted is approximately equal to the radiation absorbed. This is also depending on the emissivity and absorptivity of the surface.
As the MuPix chips are heated and have a higher temperature than the surrounding, there is a heat radiation which is given to the environment. With the expected maximal temperature of 70◦C the heat radiation ˙Qrad can be computed with the Stefan-Boltzmann law (see equa- tion (3.12)). The different material used for the measurement and the simulation have different emissivity . For the measurement with the thermal camera a black coating (NEXTEL) has been applied with an emissivity of 0.98.
Comparing the resulting radiation emitted by the heated chips without a coating it is neglectable compared to a heat dissipation of 1.8 W. With the NEXTEL coating the radiation is around 6 % of the total heat dissipation. This estimation is neglecting the heat absorption from the environment, which would even more decrease the heat loss from radiation. Therefore, the heat radiation is mostly neglected for the simulation and the measurements. During the measure- ments this was verified using an aluminium foil with the bright side over the mockup to reflect the radiation.
Q˙ =·σ·A·T4 (3.12)
Table 3.2: Data used for the heat radiation estimation.
Property Value Unit Source
Area 4.6 cm2
Temperature 343.15 [K]
Emissivity Steel 0.07 [−] [11]
Emissivity Silicon 0.1 [−] [15]
Emissivity NEXTEL 0.98 [−] [16]
Stefan-Boltzmann-constant σ 5.67·10−8 [W/m2T4] Radiation Steel ˙Q 25.3·10−3 [W]
Radiation Silicon ˙Q 36.2·10−3 [W]
Radiation NEXTEL ˙Q 108.5·10−3 [W]
3.6 Cooling analysis
3.6 Cooling analysis
The relevant non-dimensional numbers for the cooling estimations are Nusslet, Prandtl, Reynolds and to some extend the Biot number. The Reynolds number has already been analysed and emphasises a laminar flow through the gap. With this information the Nusselt number can be computed with the help of literature which finally gives the wall heat transfer coefficientα. The Prandtl number can be computed in dependence of the temperature and is easily obtained.
3.6.1 Heat transfer
The VDI-Wärmeatlas [14] has a large base of estimation for heat transfer for different cases.
For an annular gap flow there is a section, which is only considering constant wall temperatures.
For a tube there are approximations given for constant heat flux from the wall. Both cases give a similar wall heat transfer coefficient with less than 10 % deviation. Still in this section the approximation with a constant heat flux is shown which is following [14, Chapter G4].
For the diameters the definition for an annular gap flow is
Dh,g =Do−Di. (3.13)
The local Nusselt number approximation for a constant heat flux with thermal and hydrody- namic run-up for a laminar flow is
Nux,q=Nu3x,q,1+ 1 + (Nux,q,2−1)3+ Nu3x,q,31/3 (3.14) which consists of three Nusselt numbers
Nux,q,1 = 4.364 (3.15)
Nux,q,2= 1.302Re·PrDh,g x
1/3
(3.16)
Nux,q,3 = 0.459·Pr1/3ReDh,g x
1/2
. (3.17)
With equation (3.4) and equation (3.18) the wall heat transfer coefficient can be computed.
α= 1 l
Z l
0 αxdx (3.18)
The temperature for the fluid properties have been considered with a middle temperature of T = 30◦C. The influence of the material data is around 0.15 % and could be neglected as other simplification made before have higher uncertainties.
The heat dissipation of the MuPix chips is indicated as heat dissipation per surface of the chip.
The total heat ˙Qis equal to 198.7 W which gives with the area of the cylinders a corrected heat load of ˙qcor = 499.4mW/cm2 for helium. For air similar conditions were chosen to obtain a similar behaviour as with helium. The Reynolds number and the temperature increase of the air has been set to the same value as with helium. The resulting properties are shown in the following table 3.3.
Table 3.3: Data used for the estimation of the G12.
Property Helium Air Unit
Dh,g 13 [mm]
w 10 1.28 [m/s]
˙
m 2 1.87 [g/s]
Q˙ 198.7 35.8 [W]
˙
q 400 72.1 [mW/cm2]
˙
qcor 499.4 90.0 [mW/cm2]
∆Ti,o 19.1 19.1 [K]
Re(T = 30◦C) 1088 [−]
Pr(T = 30◦C) 0.66352 0.7067 [−]
Nux,q,1 4.364 [−]
Nux,q,2(T = 30◦C) 2.695·x−1/3 2.748·x−1/3 [−]
Nux,q,3(T = 30◦C) 1.4636·x−1/2 1.4913·x−1/2 [−]
Nu(T = 30◦C) 10.71 10.96 [−]
α(T = 30◦C) 126.87 21.91 [W/m2K]
The global α value shown in table 3.3 shows the magnitude of the heat transfer coefficient for helium and air. The one of helium is around six times higher than the one of air. Figure 3.6 shows the local heat transfer coefficient computed with the local Nusselt number Nux. Around x= 0 the local heat transfer coefficient goes to infinity due to the inexistent thermal boundary layer. The integral of this curve gives the global heat transfer coefficient.
The wall temperature can be computed with Tw= q˙cor
αx . (3.19)
This temperature is also shown in figure 3.6 with the temperature increase being equal for helium and air. The wall temperature is higher for air as the heat transfer coefficient is proportion of the helium to air is 5.8 which is a little higher than the one of the heat capacities which is
3.6 Cooling analysis
5.16. Still the temperature difference is under 5 K which makes the helium and air measurement comparable. The expected temperature with helium and a heat flux of 400mW/cm2 is around 70◦C which is just in the set boundaries. But there are some simplification as the overlap which will probably cause higher temperatures.
0 10 20 30 40 50 60 70 80 90 100 110 120
0 50 100 150 200 250
Position along the layer x[mm]
Localheattransfercoefficientαx[W/m2K]
(a) Heat transfer coefficient
Helium Air
0 10 20 30 40 50 60 70 80 90 100 110 120
0 10 20 30 40 50 60 70
Position along the layer x[mm]
TemperatureT[◦ C]
(b) Temperature Wall helium Wall air Fluid
Figure 3.6: Local heat transfer coefficient and resulting temperature from uniform wall heating.
3.6.2 Heat conduction in chip
In the previous section the heat transfer of an annular flow was estimated for both fluids. The chips were completely neglected and will be analysed in this section. At first the temperature increase through only one chip will be estimated followed by a heat transfer through the polymide foil. Some parts of the chip are not directly cooled and therefore the temperature is increasing compared to the cooled part of the chip. The Biot number with silicon is around 4·10−5 which shows that the heat conduction in the chip is nearly irrelevant compared to the heat transfer of
the fluid. The internal temperature could be assumed constant.
Figure 3.7a shows one silicon chip insulated on one side and cooled from a flow on the other side. The temperature at the wall can be obtained with
T1=T∞+q˙gen·ls
α (3.20)
and the temperature at the interface to the insulation with T0=T1+q˙gen·l2s
2·λ . (3.21)
As predicted with the Biot number the temperature over the thickness inside of the chip is nearly constant.
If the polymide and araldite are also considered as shown in figure 3.7b, the temperature of the chip should increase. The wall temperature is still the same as the flow conditions are assumed to be constant. The temperature between the sheets can be computed following
Tx =Tx+1+ q˙gen·ls·lx λx
. (3.22)
Figure 3.8 shows the temperature profile of both cases, with and without the araldite and polymide over the silicon chip. The difference between both cases is quite small. The major cause of temperature increase is the wall heat transfer coefficient. The polymide foil is causing a temperature increase of∼1.5 K. The temperature profile of the fluid has been scaled for better visualisation.
All dimensions used for computation and the resulting temperature are shown in table 3.4.
3.6 Cooling analysis
T∞,α Insulation
MuPix chip
qgen ls
T0 T1
˙ q
(a) Heat transfer with only one MuPix chip.
T∞,α Insulation
MuPix chip
qgen
ls T0
˙ q Araldite
Polymide
la lp T1
T2 T3
(b) Heat transfer with MuPix chip, araldite and polymide.
Figure 3.7: Heat generation inside the MuPix chip and heat transfer through the solid parts to the fluid.
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 0
10 20 30
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 0
10 20 30
ls la lp
Distance from chip [µm]
Temperature[◦ C]
Mupix chip with araldite and polymide Only MuPix chip
Figure 3.8: Temperature profile through the MuPix (silicon) chip and other solids as well as a visualisation of the fluid temperature (scaled).
Table 3.4: Properties of the conjugated heat transfer of the silicon chip.
Case Properties Silicon Steel Unit
ls 50 [µm]
la 5 [µm]
lp 50 [µm]
α 126.87 [W/m2K]
T∞ 0 [◦C]
˙
qgen 8·107 [W/m3]
λ 149 15 [W/mK]
Bi(ls) 4.2·10−5 4.2·10−5 [−]
Only chip T1 31.528 [◦C]
T0 31.529 31.535 [◦C]
Chip, araldite and polymide
T3 31.528 [◦C]
T2 33.195 [◦C]
T1 33.286 [◦C]
T0 33.286 33.299 [◦C]
Temperature increase in overlap
Over the thickness of the MuPix chip the temperature is nearly constant for silicon and steel.
But there are parts of the MuPix chip on layer 2 which are not directly cooled. This is only present on layer 2 where there is one cooling flow on the inner side. The geometry is described in section 4.2.2. Figure 3.9 shows a simplification of one MuPix of layer 2 with the green part as overlap which is not directly cooled by the flow. Assuming a constant temperature of the grey part the maximum temperature of the overlap can be computed following
Tov=TMuPix+q˙gen·l2ov
2·λ . (3.23)
The temperature increase is higher with steel due to worse heat conduction. With silicon there is still a temperature increase of 4 K while have a constant heat load. Later it will be seen that the heat dissipation in the overlap is even higher as for the grey part, causing even higher temperatures in the overlap.
3.7 Conclusions of analytical study
Insulation MuPix chip
Overlap of MuPix lov
lMuPix
ls T∞,α
TMuPix
Tov
Figure 3.9: Estimation of the temperature increase in the overlap of the MuPix chip with differ- ent materials.
Table 3.5: Properties for temperature increase in the overlap of layer 2.
Properties Silicon Steel Unit
ls 50 [µm]
lMuPix 23 [mm]
lov 4 [mm]
˙
qgen 8·107 [W/m3]
λ 149 15 [W/mK]
Bi(lov) 3.4·10−3 3.4·10−2 [−] TMuPix 33.286 31.535 [◦C]
∆T 4.30 42.67 [K]
Tov 37.58 76.20 [◦C]
3.7 Conclusions of analytical study
The results of the analytical study enhanced the understanding of the physical processes oc- curring during the cooling the MuPix chips. The knowledge could be used to build the CFD simulation model and also an estimation of the expected results for measurements and sim- ulations. The estimation of non-dimensional numbers showed that the flow will mostly be incompressible and laminar. The convection is driven by forced convection and heat radiation is neglectable with steel or silicon chips, as it is less than one percent of the total heat dissipation.
The estimation of heat transfer showed that under the assumption of a tube flow, laminar flow and constant heat dissipation, the temperature of the wall goes up to 66◦C for helium and with comparable conditions to 69◦C with air. The heat conduction analysis of the MuPix chips finally showed that a modelling of the chip with heat conduction has a major influence on the occurring temperatures as not every part has the same cooling conditions.
4 CFD Simulation
The CFD simulations of the cooling system are shown in this chapter. As there are different cooling parts which were simulated independently, the first section is giving an overview of the geometry of the different parts, the modelling and simplifications made. Furthermore, the simulation and optimisation of layers 1 & 2 is shown in section 4.2, followed by an overview of the layers 3 & 4 in section 4.3. Since the mesh of layers 3 & 4 is large, the different flows were first optimised independently and then a combined simulation of all flows with heat transfer was performed. Section 4.4 shows the optimisation of the V-folds, followed by section 4.5 and section 4.6 which are showing the optimisation of the gap flows and finally in section 4.7 the combined simulation is shown.
4.1 Overview
Figure 4.1 shows the fluid geometry of part B (centre) of the helium cooling system. There is one flow in the middle for layers 1 & 2 which are shorter compared to the layers 3 & 4. For layers 3 & 4 four different flows are displayed. Two of them flow between the layers or other detectors and are exiting into a global flow which is not shown here. Additionally, there are two flows in the V-folds. The V-folds and the G12 are not exiting into the global flow but sucked out through tubes. The pressure difference between those flows and the surrounding can therefore be controlled with the outlet pressure level. The whole cooling scheme is shown in figure 2.2 on page 10 which additionally to part B (centre) is also displaying the up- and downstream part A & C. The mass flow through the different sections is shown in table 2.3.
Gap layer 1 & 2
Gap layer 3 & SciFi
Gap layer 3 & 4 V-Folds layer 4
V-Folds layer 3
Figure 4.1: Fluid geometries of layer 1 to 4 in the centre part.
In this chapter many acronyms are used to describe the different flows and are summarised here:
V3 V-fold of layer 3 V34 V-fold of layers 3 & 4 V4 V-fold of layer 3
G12 gap flow between layers 1 & 2 G34 gap flow between layers 3 & 4 G3S gap flow between layer 3 & SciFi G3T gap flow between layer 3 & tile detector Part A Upstream layers 3 & 4
Part B Center layers 3 & 4 Part C Downstream layers 3 & 4
The fluid geometries shown in this chapter have all been constructed based on the Computer- aided design (CAD) geometry. The flow geometry was designed by Silvan Streuli from PSI who has also designed most of the detector construction. Some parts were later adapted as non negligible simplifications were found. Solid geometry as the silicon chips or some of the polymide layers have been simplified to reduce the complexity of the model.
